Mechanisms of geometric cognition

basic information

Title: Mechanisms of Geometric Cognition

Principal investigator: Mateusz Hohol, Ph.D.

Funding: National Science Centre, Poland

Grant ID: 2015/19/B/HS1/03310 (OPUS Programme)

brief description

The project aims at identifying the mechanisms of geometric cognition. It will help to explain human geometric skills and develop methodological base for the cognitive science of geometry. In particular, emphasis will be put on the analysis of the role of language in transition from the biological basis of spatial orientation to the use of advanced Euclidean geometry.

The project is interdisciplinary – it will be implemented at the intersection of cognitive science, psychology, philosophy of mathematics and methodology of science. Mechanisms of spatial orientation, results of developmental psychology research concerning acquisition of geometric skills, language of geometry characterized by the repetition of certain formulas, mechanisms of abstraction, as well as mechanisms of precision and conceptual stability in geometry will be analyzed in succeeding stages of the project. In the last stage of the project links between the mechanisms of geometric and numerical cognition will be examined.

Modern cognitive science of mathematics has its origin in the psychological studies of the representation and processing of numbers, which have been conducted since the sixties. On the other hand, geometry is an area neglected by cognitive scientists. This state of research is unsatisfactory if only due to the fact that geometric thinking is extremely important in modern mathematics, and it played an important role in the development of this discipline.

Implementation of the project can contribute to initiation of fruitful interdisciplinary discussions between cognitive scientists, philosophers and mathematicians themselves. The latter often are skeptical about the psychological and cognitive theories explaining the nature of mathematical cognition. Mathematicians point to the gap resulting from the fragmentation of theories that have concerned the numerical structures, at the same time neglecting geometry. In a wider perspective, the project may be valuable for the whole cognitive science, shedding new light on relations between the phylogenetically old spatial skills and language.

book monograph

The cognitive foundations of geometry have puzzled academics for a long time, and even today are mostly unknown to many scholars, including mathematical cognition researchers.

Foundations of Geometric Cognition shows that basic geometric skills are deeply hardwired in the visuospatial cognitive capacities of our brains, namely spatial navigation and object recognition. These capacities, shared with non-human animals and appearing in early stages of the human ontogeny, cannot, however, fully explain a uniquely human form of geometric cognition. In the book, Hohol argues that Euclidean geometry would not be possible without the human capacity to create and use abstract concepts, demonstrating how language and diagrams provide cognitive scaffolding for abstract geometric thinking, within a context of Euclidean system of thought.

Taking an interdisciplinary approach and drawing on research from diverse fields including psychology, cognitive science, and mathematics, this book is a must-read for cognitive psychologists and cognitive scientists of mathematics, alongside anyone interested in mathematical education or the philosophical and historical aspects of geometry.